The claim as I understand it is that there is no “memory” at all. What we experience as memories are simply input parameters that signal our brain to begin a particular function. In the way a neural net does not “remember” the training data but carries out what it “learned” anyway. I have problems explaining this idea as I think it is full of holes and would require some fundamental changes in how we think about feedback structures (I mean this neurologically as well as mathematical/computational).
Either way if most people don’t doubt memory storage in neurons then they are very quite about it. I’ve rarely ever read an argument for memory storage mechanisms in the brain. A good reason for this is simply the question: Where is it then? Neurons individually can’t really provide this sort of expansive data storage. And what they seem to be able to account for is too little and too widely spaced apart. Interestingly this spacing also provides a counter argument against the complex processing that would be required if there wasn’t a memory mechanism.
Personally I think the dismissal of memory comes with a lot of hubris attached, as well as a total lack of understanding information theory. Information theory itself seems to be popularly bemoaned by neuroscientist as well. But it’s hard to see the alternative and is a bit paradoxical since the only way I can seem to understand the “no memory” claim is by using a computer neural net metaphor.